Shape resonances definition

A possible role for shape resonances has been postulated in a number of the photoionization studies mentioned above [52, 53, 57, 60], although it has to be noted that except for camphor [57], the evidence for the existence of the shape resonance is not definitive. (It also then remains an open question how any such resonances, inferred from fixed geometry calculations, would manifest themselves in practice in large, and sometimes floppy, molecules, such as these chiral species.)... 

Free radicals with resonance are definitely planar, though triphenylmethyl-type radicals are propeller shaped, like the analogous carbocations (p. 225). 

The interest in semiconductor QD s as NLO materials has resulted from the recent theoretical predictions of strong optical nonlinearities for materials having three dimensional quantum confinement (QC) of electrons (e) and holes (h) (2,29,20). QC whether in one, two or three dimensions increases the stability of the exciton compared to the bulk semiconductor and as a result, the exciton resonances remain well resolved at room temperature. The physics framework in which the optical nonlinearities of QD s are couched involves the third order term of the electrical susceptibility (called X )) for semiconductor nanocrystallites (these particles will be referred to as nanocrystallites because of the perfect uniformity in size and shape that distinguishes them from other clusters where these characteriestics may vary, but these crystallites are definitely of molecular size and character and a cluster description is the most appropriate) exhibiting QC in all three dimensions. (Second order nonlinearites are not considered here since they are generally small in the systems under consideration.)... 

The a-substituted tropolonates 2 which are tris chelate complexes with a M06 coordination core have received considerable study by DNMR.27, 4S 46) The complexes are of the M(A-B)3 and M(A-B )3 types and therefore the averaging sets of Eaton efa/.26, 27 in Table 1 are applicable. The metal ions and a-R-substituents used in these studies include M = Al(III), Ga(III), Co(III), V(III), Mn(III), Ru(III), Rh(III) and Ge(IV) R = isopropyl (C3H7) and isopropenyl (C3HS), however, only complexes of Al(III), Ga(III), and Co(III) have yielded definitive mechanistic information.27, 45 46> On the basis of line shape changes of the methyl resonances these complexes can be classed kinetically as follows stereochemically nonrigid complexes which attain the fast-exchange limit of inversion and/or isomerization... 

Now that the range of likely shapes has been defined by experiments on related molecules and by energy calculations, we focus on the details of specific structures that have been observed for real, crystalline cellulose molecules, primarily by x-ray, neutron, and electron diffraction studies. A number of landmark concepts have been established with electron microscopy, as well. Infrared (IR), Raman, and nuclear magnetic resonance (NMR) spectroscopy have all also been important in the quest for understanding cellulose structure. Such data, while so far not able to provide complete definitive structures themselves, constitutes additional criteria that any proposed structure must be able to explain. In addition, unlike crystallography, the resolution of spectroscopic methods is not directly affected by the dimensions of the... 

The orientational distribution fimction P (cos 0) enters the shape of the wideline spectrum 5(f2) in a slightly hidden way. The angular dependence of the resonance frequency is given by (3.1.23) via the orientation of the magnetic field in the principal axes system XYZ of the coupling tensor (cf. Fig. 3.1.2), while the orientational distribution function specifies the distribution of the preferential direction n in a molecule-fixed coordinate frame (Fig. 3.2.2(a)). Figure 3.2.3 shows the relationship between the different coordinate frames and the definition of the relative orientation angles. 

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